Analog Servos
Analog RC servos use a form of pulse width modulation (PWM) to control the speed of the servo. It's basically switch the motor on and off quickly (Commonly 50 times per second). The motor rotates a certain angle depending on the width of the on-pulse.
Digital servos
Digital servos also use PWM, but at a much higher frequency (6 times that of a analog servo). They contain a microprocessor that received the signal, and then send the PWM to the motor
Comparison
The digital motor will be smooth and react faster, but it's more complex and therefore more expensive [1]: https://upload.wikimedia.org/wikipedia/commons/7/7b/ServoPwm.png